Model Thinking Part 1- Coarsera

Model thinking – Scoot E. Page – U. of Michigan

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Reasons to Model

• Predict points
• Understand data
• Understand patterns — class of outcome
• Design solutions

Shelling Segregation Model

• Sorting (be with people you like) and peer influence (homophily)  (act like people you are with)  on behavior
• model is agent based, consisting of agent, behavior, and aggregation
• Shelling threshold based — tipping (move tipping: exodus tip (move out), genesis (move in)
• micro behavior is not the same as macro aggregation, hence people individually may be tolerant (micro) but resulting population movement (macro may produce segregation.

Granovettor’s Model

Model is N individuals, Each N has a threshold: T (j) for person j, join if T (j) other join e.g.: 0,1,2,3,4 — all will join since 0 for sure joins

This tells us that lower thresholds and more variation in thresholds can have large  effects.

Standing Ovation Model

extension to Granovettor’s Model

partially caused by peer effect (homophily) and information

Model rules:

• Threshold to stand: T
• Quality: Q
• Signal S=Q+E (error of diversity)
• Initial Rule: S > TG; Subsequent rule standup if more X% (E) stand up

Why standing ovation:

• higher quality
• lower threshold\larger peer effect
• more variation (E)
• Celebrity
• group size

This model (and others) is a way to determining results in situations.

Note that deciding if a sorting effect or peer effect from a snap shoot of state is difficult to determine, hence additional dynamic data to see what was major cause —  hence more dynamic data meed in model to explain what movement (sorting) or neighbor influence (peer) caused change.

Aggregation

Philip Anderson – “More is Different” – emergent properties at macro level

Aggregation of data

Independent decisions

Central Limit Theorem

Assumes independent events and finite (limited range) variance

Probability is a normal (Gaussian) distribution (looks like a bell curve) with likely outcome  at the mean
plus/minus 1 Standard deviation (sigma) cover 68% in a normal curve; plus/minus 2 standard deviations cover 95%; plus/minus 3 standard deviations cover 99.75% of possible outcomes

Binomial Theorem example if N/2 is the mean, then SD is (square root of N / 2), so N = 100 = 100/ 2 = 50, SD is 10/2 (sq root of 100) / 2) = 5

6Sigma = 3.4 errors out of 1,000,000 events

Cellular Automaton– self organization, emergence — some level of functionality such as glider; get logic right

Game of Life — Rules:  If off,  turn on if 3 neighbors on; if on, stay on if 2 or 3 neighbors on

Preferences

Transitive Preference order, rational preferences, collective preferences – social sense this is called rational

all individual are rational but the aggregate can be non-transitive — this is called Condorcet’s paradox

Decision Making

For multidimensional decision making:

• Qualitative – use matrix
• Quantitative – use matrix plus weights

For Spatial Chose models: select ideal point (single or multidimensional) for a good, then  determine values for each decision point possibility , than a see difference from  ideal point and add up the differences.  The difference between the ideal points and the computed points determines which is the closest decision point possibility.  Come back to this and clarify.

Probability

• outcome is a set of things that can happen
• event is a subset of outcomes.

3 axions

• probability of an event is between 0 and 1 — could also be 0 or 1
• Sum of all possible outcomes = 1
• If A is subset of B, then p(A) is less than or equal to  p(B) or p(B) is greater than or equal to p(A)

3 types of  statistics:

• Classical (e.g., dice and coin flips — can prove mathematically
• Frequency (estimating frequency by counting data – how often has something happend? – assumes stationarity (nothing has changed),
• Subjective (estimate but base on model)